CHAPTER 01

INTRODUCTION

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1.1 INTRODUCTION

The purpose of this thesis is to investigate the minor loss of water when flowing through 90° bend in locally available PVC pipes of different dimensions. In addition to this, head loss and minor loss coefficients of these pipes are ascertained. Losses occur in any straight pipes and ducts are referred as major (frictional) losses and in system components (elbows, valves, bends, tees, etc.) are referred as minor losses. Minor loss coefficients determined in this thesis will help to establish more convenient use of locally made pipes in local industries.

1.2 REQUIREMENT OF THE THESIS

90° bends are used in the piping units of pumps or engines. The standard values of minor loss coefficients of various dimensional pipes are available in many pipe hand books & internet. But minor loss coefficients of locally made pipes are not available. So, this thesis is performed with a view to determine the minor loss coefficients for locally made pipes of different diameters ( 0.5 inch, 0.75 inch and 1.0 inch )

1.3 PREVIOUS WORKS

In the context of our study, there are some contributions of particular importance. M.H. Khan and Md. Quamrul Islam [4] made an experimental investigation of flow through flexible pipes and bends. In their work, they used metal made flexible pipes with diameters of 2 inch, 3.5 inch, 4 inch and 5 inch. Two manometers were used: one for trough to trough and one for crest to crest readings.

Md. Rizwan, Md. Ishfak and Pranay [9] did their work on locally made RRR pipes and bends to measure friction factor and minor loss coefficient respectively.

Md. Hafiz, Roy and Hossain [8] determined minor head loss and friction factor for locally available PVC pipe 90°.

Mr. Jaiman, Oakley and Adkins [5] did CFD modeling of corrugated flexible pipes. In their work they constructed a numerical model of the corrugated flexible pipe and did simulation to show variation of velocity distribution throughout the pipe.

Md. Rokounzzaman, Md. Saad and A.S.M. Jonayat determined the friction factor of locally made flexible pipes and minor loss coefficient of flexible bends.

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1.4 OUTLINE OF THE THESIS

This thesis essentially consists of –

Brief information about head loss and minor loss coefficient.

Data table for locally available bends of different dimensions (1.0 inch, 0.75 inch & 0.50 inch diameter) at bend angle of 90°.

Manifestation of experimental results in tabular and graphical form

Discussion on findings and recommendations.

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CHAPTER 02

FUNDAMENTAL AND GENERAL THEORY

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2.1 BACKGROUND AND THEORY

In laminar flow, the fluid particles move along straight parallel paths in layers or laminae, such that the paths of individual fluid particles do not cross those of the neighboring particles. It occurs at low velocity so that forces due to viscosity predominate over the inertial force. The viscosity of fluid induces relative motion within the fluid as the fluid layers slide over each other, which in turn gives rise to shear stress. The magnitude of the shear stress so produced, varies from point to point, being maximum at the pipe wall and gradually decreasing with increase in the distance from the wall. The shear stress results in developing a resistance to flow. In order to overcome this shear resistance the pressure drops from section to section in the direction of flow. This in turn causes a pressure gradient to develop.

According to the theory of fluid friction for laminar flow, the frictional resistance in the

laminar flow is-

1. Proportional to the velocity of the flow

2. Independent of the pressure

3. Proportional to the area of surface in contact

4. Independent of the nature of the surface in contact

5. Greatly affected by the variation of the temperature of the flowing fluid

Mostly the flow in pipes is turbulent. Turbulent flow is characterized by random, disorganized motion of the particles, from side to side across the pipe as well as along its length. There will, however, always be a layer of laminar flow at the pipe wall- the so-called 'boundary layer'. If Reynolds number is greater than 4000 the flow is turbulent. The velocity distribution in turbulent flow is relatively uniform and the velocity profile of the turbulent flow is much flatter than the corresponding laminar flow parabola for the same mean velocity. It becomes even flatter with increasing Reynolds number as shown in the figure-

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Figure 2.1: Velocity distribution in laminar and turbulent flow

In turbulent flow, the fluid particles are in an extreme state of disorder. Their movement is haphazard and large scale eddies are developed, which results in a complete mixing of the fluid. Such irregular motions of fluid panicles in turbulent flow is on account of the fact that, at any fixed point, the velocity and the pressure do not remain constant with time, but fluctuate in an irregular manner. In other words, in turbulent flow there are irregular velocity and pressure fluctuations of high frequency superimposed on the main flow.

According to the theory of friction for turbulent flow, the frictional resistance in the case of turbulent flow is

Proportional to (velocity) ⁿ, where the index n varies from 1.72 to 2 Independent of the pressure Proportional to the density of flowing fluid Slightly affected by the variation of the temperature of flowing fluid Proportional to the area of surface in contact Dependent of the nature of the surface in contact

The overall head loss for a pipe system consists of the head loss due to the viscous effects in straight pipes, named the major loss and denoted by hf(major) and the head loss occurred in the various pipe components (elbow, valve, bend etc.) named the minor loss and denoted by hf(minor). The sum of both these losses make up the total head loss.

hf(total)= hf(major) + hf(minor)

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These terms should not be misled by the terms major and minor because they do not necessarily reflect the relative importance of each type of loss. For instance, in piping system which is short but contains many components, it is expected that the minor losses to be much greater than the major losses. It is often necessary to determine the head losses hf(major) and hf(minor), that occur in a pipe flow so that the energy equation can be used in the analysis of pipe flow problems.

The minor losses are due to below mentioned reasons,

Pipe entrance and exit. Sudden expansion and contraction. Bends, elbow, tees and others fittings. Valves, open or partially closed. Gradual expansions or contraction.

Minor loss in a bend is due to flow separation on the curved walls and a swirling secondary flow arising from the centripetal acceleration.

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2.2 MINOR LOSSES

The losses that occur in pipelines due to reducers, bends, elbows, joints, valves etc. are called minor losses. This is a misnomer because in many cases these losses are more important than the losses due to pipe friction. For all minor losses in turbulent flow, the head loss varies as the square of the velocity. Thus a convenient method of expressing the minor losses in flow is by means of a loss coefficient. Values of the loss coefficient for typical situations and fittings are found in standard handbooks. The form of Darcy's equation used to calculate minor losses of individual fluid system components is expressed by the equation

hm= K v ²2 g …………………………………………………..(2.2.1)

Where, hm = minor loss for a fitting

K = minor loss coefficient

v = velocity of the fluid for the time

So for a given place minor loss coefficient K depends on velocity v. Increase in velocity will decrease the value of K. Although K appears to be a constant coefficient, it varies with different flow conditions. Factors affecting the value of K include-

1. The exact geometry of the component2. The Reynolds number 3. Proximity to other fittings, etc. (Tabulated values of K are for components in isolation

- with long straight runs of pipe upstream and downstream).

Since the losses of energy are found to vary as the square of the mean velocity of the flow, the minor losses are frequently expressed in terms of the velocity head of the flowing liquid. Some of losses of energy which may be caused due to the change of velocity are as indicated below-

1. Loss of energy due to sudden enlargement2. Loss of energy due to sudden contraction3. Loss of energy at the entrance to a pipe from the large vessel 4. Loss of energy at the exit of a pipe5. Loss of energy due to an obstruction in the flow passage

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2.3: WHY BENDS ARE USED IN A PIPELINE

Bends are provided in pipes to change the direction of flow through it. An additional loss of

head, apart from that due to fluid friction, takes place in the course of flow through pipe bend.

The fluid takes a curved path while flowing through a pipe bend as shown in figure 2.6.

Whenever a fluid flows in a curved path, there must be a force acting radially inwards on the

fluid to provide the inward acceleration, known as centripetal acceleration. This results in an

increase in pressure near the outer wall of the bend, starting at some point A and rising to a

maximum at some point B. There is also a reduction of pressure near the inner wall giving a

minimum pressure at C and a subsequent rise from C to D. Therefore between A and B and

between C and D the fluid experiences an adverse pressure gradient (the pressure increases in the

direction of flow).

Figure 2.2: Flow through a bend.

Fluid particles in this region, because of their close proximity to the wall, have low velocities and

cannot overcome the adverse pressure gradient and this leads to a separation of flow from the

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boundary and consequent losses of energy in generating local eddies. Losses also take place due

to a secondary flow in the radial plane of the pipe because of a change in pressure in the radial

depth of the pipe. This flow, in conjunction with the main flow, produces a typical spiral motion

of the fluid which persists even for a downstream distance of fifty times the pipe diameter from

the central plane of the bend. This spiral motion of the fluid increases the local flow velocity and

the velocity gradient at the pipe wall, and therefore results in a greater frictional loss of head than

that which occurs for the same rate of flow in a straight pipe of the same length and diameter.

The additional loss of head (apart from that due to usual friction) in flow through pipe bends is

known as bend loss and is usually expressed as a fraction of the velocity head as K v ²2g , where vis

the average velocity of flow through the pipe. The value of K depends on the total length of the

bend and the ratio of radius of curvature of the bend and pipe diameter R/D. The radius of

curvature R is usually taken as the radius of curvature of the centre line of the bend. The factor K

varies slightly with Reynolds number NRe in the typical range of NRe encountered in practice, but

increases with surface roughness.

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2.4: EQUATION OF HEAD LOSS IN 90°BEND

The 90° bend is provided in a flow passage to change the direction of flow. The change in

direction of flow also results in causing loss of energy. The loss of energy in the 90° bend is due

to the separation of flow from the boundary and consequent formation of eddies resulting in the

dissipation of energy in turbulence. In general the loss of head in 90° bend provided in pipes may

be expressed as-

hm= K v ²2 g ………………………………………………..(2.4.1)

Where K is called minor loss coefficient and v is the mean velocity of flow of fluid. The value of

K however depends on the total angle of the 90° bend and on relative radius of curvature R/D,

where R is the radius of curvature of the pipe axis and D is the diameter of the pipe.

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Figure 2.3: 90° bended pipe with manometer.

Assumptions

Incompressible fluid

Steady flow

No slip condition at the surface

Applying Bernoulli’s equation between section 1-1 and 2-2 at figure

p ₁γ + v ₁²

2g + Z₁ = p₂γ + v ₂²

2g + Z2

Or, p ₁γ - p ₂

γ = v ₂²2g - v ₁²

2g + Z2– Z1

Or, p ₁γ - p ₂

γ = v ₂²2g - v ₁²

2g + 0

Or, p ₁γ - p ₂

γ = v ₂²2g - v ₁²

2g ………………………………………………

( 2.4.2)

Here, p1 = pressure of fluid at inlet

p2 = pressure of fluid at outlet

v1 = velocity of fluid at inlet

v2 = velocity of fluid at outlet

Now from manometry,

p1 + γ ( H + Hm) = p2 + γ H + γmHm

So, p₁γ - p₂

γ = Hm( γ mγ – 1) …………………………………………………( 2.4.3)

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Here, γm = specific weight of manometric fluid

γ = specific weight of water

Hm = deflection of manometric fluid

From equation (2.3.2) & (2.3.3),

v ₂²2g - v ₁²

2g = Hm( γ mγ – 1)

Or, hf = Hm( γ mγ – 1) ……………………………………………………(2.4.4)

Let us consider v1= v, v2 = v2

Or,v ₂²2g - v ²

2 g = Hm( γ mγ – 1)

Or, v ²2g ( v ₂²

v ² -1 ) = Hm ( γ mγ – 1)

So, hm= K v ²2 g ……………………………………………………………(2.4.5)

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CHAPTER 03

EXPERIMENTAL SETUP AND SPECIMEN DETAILS

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3.1 EXPERIMENTAL SETUP

Figure 3.1: Diagram of experimental setup.

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Gate valve

90° bend

ManometerMain supply

Discharging pipe

3.2 APPARATUS & OTHER INSTRUMENTS USED

The apparatus used in the experiment are listed below:

90° bends (4 90° bends: 2.0-1.50 inch, 2.0-1.0 inch, 1.0-0.75 inch, 1.0 inch- 0.50 inch) Material: Galvanized iron.

Gate Valves Plastic Pipes U-tube manometer (working fluid: Mercury) Bucket Weight Measuring Instrument (Platform Scale) Centrifugal Pump Thread Tape Adhesive (Araldite) Stopwatch Nipple Joint Thermometer Pipe Wrench Pressure Tapping

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3.3 SPECIMEN DETAILS

3.3.1 90°Bends

A bend is a pipe fittings installed between two lengths of pipe or tubing to allow a change odf direction. An elbow is a specific, standard, engineered bend, usally of 90° or 45° angle. The ends may be machined for butt welding , threaded or socketed.

Figure 3.2: Schematic of 90° Bend

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Figure 3.3: 90° Bend

3.3.2 Gate Valve

The gate valve, also known as a sluice valve, is a valve that opens by lifting a round or rectangular gate/ edge out of the path of the fluid. The distinct feature of a gate valve is the sealing surfaces between the gate and seats are planar, so gate valves are often used when straight-line flow of fluid and minimum restriction is desired. The gate faces can form a wedge shape or they can be parallel. Gate valves are primarily used to permit or prevent the flow of liquids, but typical gate valves shouldn't be used for regulating flow, unless they are specifically designed for that purpose. Because of their ability to cut through liquids, gate valves are often used in the petroleum industry. On opening the gate valve, the flow path is enlarged in a highly nonlinear manner with respect to percent of opening. This means that flow rate does not change evenly with stem travel. Also, a partially open gate disk tends to vibrate from the fluid flow. Most of the flow change occurs near shutoff with a relatively high fluid velocity causing disk and seat wear and eventual leakage if used to regulate flow. Typical gate valves are designed to be fully opened or closed. When fully open, the typical gate valve has no obstruction in the flow path, resulting in very low friction loss.

Figure 3.4: Gate Valve

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Gate valves are characterized as having either a rising or non-rising stem. Rising stems provide a visual indication of valve position because the stem is attached to the gate such that the gate and stem rise and lower together as the valve is operated. Non-rising stemvalves may have a pointer threaded onto the upper end of the stem to indicate valveposition, since the gate travels up or down the stem on the threads without raising or lowering the stem. Non-rising stems are used underground or where vertical space is limited.

3.3.3 Manometer

A manometer refers to a pressure measuring instrument usually limited to measuring pressures near to atmospheric. The term manometer is often used to refer specifically to liquid column hydrostatic instruments. It may be of various types. In our experiment, U-tube liquid column differential manometer is used.

Liquid column gauges consist of a vertical column of liquid in a tube that has ends which are exposed to different pressures. The column will rise or fall until its weight is in equilibrium with the pressure differential between the two ends of the tube. A very simple version is a U-shaped tube half-full of liquid, one side of which is connected to the region of interest while the reference pressure (which might be the atmospheric pressure or a vacuum) is applied to the other. The difference in liquid level represents the applied pressure.

The pressure exerted by a column of fluid of height h and density p is given by the hydrostatic pressure equation, P = hug. Therefore the pressure difference between the applied pressure P2 and the reference pressure P1 in a U-tube manometer used in the experiment can be found by solving P2 – P1 = hug. In other words, the pressure on either end of the liquid (shown in blue in the figure to the right) must be balanced (since the liquid is static) and so it can be found P2 = P1 + hug.

If the fluid being measured is significantly dense, hydrostatic corrections may have to be made for the height between the moving surface of the manometer working fluid and the location where the pressure measurement is desired except when measuring differential pressure of a fluid (for example across an orifice plate or venturi), in which case the density ρ should be corrected by subtracting the density of the fluid being measured.

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Figure 3.5: U-tube manometer

In our experiment, we have used mercury (Hg) as the working fluid of the manometer. Mercury is preferable when manometer deflection is moderate. Mercury was good and handy between the ranges of pressure we have dealt with in our experiment.

3.3.4 Manometric Fluid Carbon Tetra Chloride (CCl4):

We have used Carbon Tetra Chlorideas the manometric fluid.Although any fluid can be used, mercury is preferred for its high density (1590 kg/ m3) and low vapor pressure. For low pressure differences well above the vapor pressure of water, water is commonly used (and "inches of water" is a common pressure unit). Liquid-column pressure gauges are independent of the type of gas being measured and have a highly linear calibration. They have poor dynamic response. When measuring vacuum, the working liquid may evaporate and contaminate the vacuum if its vapor pressure is too high, When measuring liquid pressure, a loop filled with gas or a light fluid can isolate the liquids to prevent them from mixing but this can be unnecessary, for example when mercury is used as the manometer fluid to measure differential pressure of a fluid such as

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water. Simple hydrostatic gauges can measure pressures ranging from a few Torr (a few 100 Pa) to a few atmospheres (approximately 1,000,000 Pa). The CCl4 was colored by Iodine to separate it from water.

3.3.5 Thread Seal Tapes:

Thread seal tape commonly known as “Teflon tape", "Tape dope" or “plumber's tape” is a polytetrafluoroethylene (PTFE) film cut to specific widths for use in sealing pipe threads. The tape is wrapped around the exposed threads of a pipe before it is screwed into place. Since the PTFE is malleable, deformable and impermeable, it acts a little like putty under compression, being forced into small gaps between threads in order to create an air and watertight seal when threaded into a joint. Thread tape is appropriate for use on tapered threads, where it is the thread itself that provides the seal surface. It is not required on parallel threads; parallel threads will not seal effectively themselves, even with tape. The sealing force on a tapered thread comes about from wedge action that of a parallel thread is merely the axial force from the nut and is inadequate for a good seal. For this reason parallel threads are only used to mechanically clamp some other form of seal (e.g. a metallic pipe olive, or a flat face with a conformable washer against it). These seals do not require additional tape, and applying tape to their threads has no purpose.

Figure 3.6: Thread Seal Tapes

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There are two US standards for determining the quality of any PTFE tape. MIL-T-27730A (an obsolete military specification still commonly used in industry in the US) requires a minimum thickness of 3.5 mils and a minimum PTFE purity of 99%.

The second standard, A-A-58092, is a commercial grade which maintains the thickness requirement of MIL-T-27730A and adds a minimum density of 1.2 g/cc. Relevant standards may vary between industries; tape for gas fittings (to (UK gas regulations) is required to be thicker than that for water. Although PTFE itself is suitable for use with high-pressure oxygen, the grade of tape must also be known to be free from grease.

3.3.6 Platform Scale:

Platform scales are instruments used for measuring weight. It may be various types. In our experiment portable beam scale type platform scale was used. These quality portable beam scales are designed specifically for industrial applications. HB series scales are constructed of heavy duty cast iron with corrosion resistant loops, bearings and nose irons. Wheels make the scale easy in move and relocate to accommodate alternative work sites. Beams are graduated on the front and rear with weight indicated at the center of the poise.

Figure 3.7: Platform Scale

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3.3.7 Nipple Joint:

A nipple is defined as being a short stub of pipe which has external male pipe threads at each end, for connecting two other fittings. Nipples are commonly used for plumbing and hoses and second as valves for funnels and pipes. They are usually threaded steel, brass, chlorinated polyvinyl chloride (CPVC) or copper; occasionally just bare copper.

The length of the nipple is usually specified by the overall length with threads. It may have a hex section in the center for wrench to grasp. A "close nipple" has no unthreaded area; when screwed tightly between two female fittings, very little of the nipple remains exposed.

A close nipple can only be unscrewed by gripping one threaded end with a pipe wrench which will damage the threads and necessitate replacing the nipple, or by using a specialty tool known as a nipple wrench (or known as an internal pipe wrench) which grips the inside of the pipe, leaving the threads undamaged. When the ends are of two different sizes it is called a reducer or unequal nipple. A barrel nipple or a pipe nipple is one which is usually made from pipe and is threaded only at both ends.

Figure 3.8: Nipple Joint

3.3.8 Adhesives:

Araldite is an engineering and structural epoxy, acrylic and polyurethane adhesives. Highmark manufacturing uses Araldite in the manufacture of advanced ballistic protection body armor. Araldite was used to bond columns and fins.

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3.3.9 Stopwatch:

A stopwatch is a handheld timepiece designed to measure the amount of time elapsed from a particular time when activated to when the piece is deactivated. A large digital version of a stopwatch designed for viewing at a distance, as in a sports stadium, is called a stop clock.

The timing functions are traditionally controlled by two buttons on the case. Pressing the top button starts the timer running, and pressing the button a second time stops it, leaving the elapsed time displayed. A press of the second button then resets the stopwatch to zero. The second button is also used to record split times or lap times. When the split time button is pressed while the watch is running, the display freezes, allowing the elapsed time to that point to be read, but the watch mechanism continues running to record total elapsed time. Pressing the split button a second time allows the watch to resume display of total time.

Figure 3.9: Stopwatch

Digital electronic stopwatches are available which, due to their crystal oscillator timing element, are much more accurate than mechanical timepieces. Because they contain a microchip, they often include date and time-of-day functions as well. Some may have a connector for external sensors, allowing the stopwatch to be triggered by external events, thusmeasuring elapsed time far more accurately than ispossible by pressing the buttons with One's finger.

Nowadays cell phones are featured with digital stopwatch and we have use this because of its ease of use and handiness.

The device is used when time periods must be measured precisely and with a minimum of complications. Laboratory experiments and sporting events like sprints are good examples.

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3.3.10. Plastic Pipes

A pipe is a tubular section or hollow cylinder, usually but not necessarily of circular cross-section, used mainly to convey substances which can flow — liquids and gases (fluids), slurries, powders, masses of small solids. It can also be used for structural applications; hollow pipe is far stiffer per unit weight than solid members.

Figure 3.10: PVC Pipes

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3.4PROCEDURE

Below are the steps followed in the experiment

3.4.1 Specimen Preparation:

1. One PVC pipe (2.0 inch) is selected corresponding to the diameter of supply side line and threads were cut in at the end of the PVC pipe to be fitted with line.

2. Other side of the PVC pipe is fitted with one of the 90° bends under experiment. The downstream side of the 90° is also fitted with another PVC pipe of corresponding diameter.

3. The downstream side pipe is fitted with a gate valve to control the downstream flow.

4. Now using drill machine, two drills transverse to the pipe's length were made at two modes where manometers are required to be connected with pipe nipples. Joints were tightened by using thread seal tapes.

5. Steps 1 to 4 were repeated for another three 90° bends.

6. Now required machining operations are done; specimen were properly washed and cleaned to eliminate dirt, oil and other undesirable internal surface matter.

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3.4.2 Construction Setup:

1. Downstream end of the 90° bend was connected with the PVC pipe which is connected to the gate valve with supply pipe.

2. Thread tapes were used to ensure proper sealing in different connections.

3. The other end of the downstream pipe was directed to the bucket through a flexible pipe to ensure that the hole piping system is filled with water.

4. After preparing the manometer, manometric fluid (carbon tetra chloride) was injected to it.

5. The limbs of manometer were connected to the nipples attached to the specimen through flexible tubes and fine wires were used to ensure proper sealing.

6. Priming of the manometer was performed.

7. One stand was used to maintain the specimen horizontal and wood piece was used to keep the discharge end at elevated height to ensure full flow of water.

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3.4.3 Data Collection Procedure:

1. At first, the inner diameter of the specimen was measured.

2. The room temperature was observed.

3. Mass of empty bucket was measured.

4. The zero level of the manometer was checked.

5. By opening the gate valve water was allowed to flow through the testing section and all the sealing was checked.

6. Now stop-watch was turned on and water flowing through the pipe was collected to the bucket.

7. Steady state manometer readings were collected.

8. After a time, stop-watch was turned off and mass of water filled bucket was measured by platform scale.

9. Stop-watch reading was taken.

10. By changing the gate valve opening flow rate was varied and reading were taken at these flow rates by repeating step to ten. These way eight readings were taken for each 90° bends.

11. The above procedure was performed for three different dimensions of 90° bends.

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CHAPTER 04

CALCULATION AND GRAPH

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4.1 NECESSARY EQUATIONS

Equations used in the calculation are mentioned below:

1. Mass Flow Rate:

Q = mt

2. Mean Velocity:

v = QAρ

3. Reynolds Number:

NRe =ρvdµ

4. Head Loss:

hm(flowingfluid)=Hm(manometric fluid )× γ m(manometric fluid )γ (flowingfluid )

5. Minor Loss Coefficient:

K = 2 ghmv ²

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4.2 CALCULATION TABLES

Table 4.1: Data for 0.50 inch GI 90° bend.

No. of observations

Manometer Reading Weight of bucket and water (kg)

Weight of Empty Bucket (kg)

Weight of Water(kg)

Time of water collection(sec)

mass flow rate (kg/sec)

Left column(inch)

Right column (inch)

1 9.375 8.75 11.8

2.4

9.4 49.69 0.18922 8.875 8.125 11.45 9.05 48.59 0.18633 8 7.25 10.9 8.5 49.39 0.17214 7.125 6.375 11.2 8.8 55.29 0.15925 6.75 6 11.25 8.85 55.81 0.15866 6.125 5.5 11.4 9.0 55.95 0.16097 5.375 4.75 11.7 9.3 67.04 0.13878 4.875 4.375 10.6 8.2 69.33 0.11839 4.5 3.75 11. 6 8.2 72.63 0.112910 3.625 3.0 11.6 9.2 82.02 0.1122

Table 4.2: Calculation table for 0.50 inch GI 90° bend.

No. of Observations

Velocity(m/s)

Reynolds Number,NRe

Head loss, hm Minor LossCoefficient,K

CCl4 (inch)

CCl4 (m) water (m)

1 1.4984 21761.9 18.125 0.4604 0.732 6.3942 1.4755 21429.3 17.00 0.4318 0.6865 6.18463 1.3630 19795.4 15.25 0.3874 0.616 6.50334 1.2609 18312.6 13.5 0.343 0.5454 6.72825 1.2561 18242.8 12.75 0.3239 0.515 6.40186 1.2743 18507.2 11.625 0.2953 0.4695 5.67077 1.0985 15953.9 10.125 0.2572 0.4089 6.6468 0.9369 13607.0 9.25 0.235 0.3736 8.34779 0.8942 12986.8 8.25 0.2096 0.3332 8.17310 0.8886 12905.5 6.625 0.1683 0.2676 6.6469

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Table 4.3: Data for 0.75 inch GI 90° bend.

No. of observation

Manometer Reading mass of bucket and water (kg)

mass of Empty Bucket (kg)

mass of Water(kg)

Time of water collection(sec)

mass flow rate (kg/sec)Left

column (inch)

Right column(inch)

1 11 11.2 10.6

2.5

8.1 10.3 0.782 10.3 10.5 12.35 9.85 14.11 0.6983 9.1 9.3 12.5 10 15.5 0.6454 8.3 8.5 13 10.5 16.66 0.635 7.3 7.7 12.15 9.65 16.18 0.5966 6.3 6.7 11.45 8.95 15.98 0.567 5.4 5.7 11.75 9.25 17.94 0.518 4.8 5 12.05 9.55 19.29 0.4959 3.6 3.9 11.5 9 20.7 0.4310 2.9 3.1 11.4 8.9 22.47 0.396

Table 4.4: Calculation table for 0.75 inch GI 90° bend.

No. of Observations

Velocity(m/s)

Reynolds Number,NRe

Head loss, hm Minor LossCoefficient,K

CCl4 (inch)

CCl4 (m) water (m)

1 2.74 59133.86 22.4 0.568 0.9 2.352 2.45 52875.17 20.8 0.528 0.84 2.743 2.27 48990.46 18.4 0.467 0.74 2.814 2.21 47695.56 16.8 0.426 0.67 2.695 2.09 45105.75 15.0 0.38 0.6 2.76 1.97 42515.95 13 0.33 0.52 2.627 1.8 38847.06 11.1 0.282 0.44 2.668 1.74 37552.16 9.8 0.25 0.39 2.529 1.51 32588.37 7.5 0.19 0.3 2. 5810 1.39 29998.56 6 0.15 0.23 2.33

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Table 4.5: Data for 1 inch GI 90° bend.

No. of observations

Manometer Reading Weight of bucket and water (kg)

Weight of Empty Bucket (kg)

Weight of Water(kg)

Time of water collection(sec)

mass flow rate (kg/sec)

Left column(inch)

Right column (inch)

1 11 11 17.4

1.55

15.85 12.77 1.292 10.2 10.2 16.6 15.05 13.23 1.133 9 8.8 15.4 13.85 13.06 1.064 8.3 8 14.3 12.75 12.93 0.9865 7.3 7 13.65 12.1 13.11 0.9236 6 5.5 12.2 10.65 12.97 0.827 4.4 4 11.25 9.7 13.31 0.798 3.5 3.25 10.5 8.95 13.58 0.669 3 2.5 9.95 8.4 13.18 0.6310 2 1.75 8.4 6.85 13.48 0.51

Table 4.6: Calculation table for 1 inch GI 90° bend.

No. of Observations

Velocity(m/s)

Reynolds Number,NRe

Head loss, hm Minor LossCoefficient,K

CCl4 (inch)

CCl4 (m) water (m)

1 2.56 73665.54 22 0.5588 0.89 2.662 2.24 64457.35 20.4 0.519 0.83 3.243 2.1 60428.76 17.8 0.45 0.72 3.24 1.95 56112.42 16.3 0.414 0.65 3.355 1.83 52659.3 14.3 0.36 0.57 3.346 1.62 46616.5 11.5 0.29 0.46 3.447 1.56 44890 8.4 0.213 0.33 2.668 1.31 37696 6.75 0.171 0.27 3.089 1.25 35969.5 5.5 0.14 0.22 2.7610 1.01 29063.35 3.75 0.095 0.15 2.88

Page | 33

4.3: GRAPHS

1.2E+04 1.4E+04 1.6E+04 1.8E+04 2.0E+04 2.2E+04 2.4E+040

0.10.20.30.40.50.60.70.8

Reynolds Number, NRe

Hea

d L

oss,

hm (

m)

Figure 4.1: Head loss, hm(experimental)vs Reynolds Number, NRe for 0.5 inch 90° bend

2.5E+04 3.0E+04 3.5E+04 4.0E+04 4.5E+04 5.0E+04 5.5E+04 6.0E+04 6.5E+040

0.10.20.30.40.50.60.70.80.9

1

Reynolds Number, NRe

Hea

d L

oss,

hm

(m)

Figure 4.2: Head loss, hm(experimental)vs Reynolds Number, NRe for 0.75 inch 90° bend

Page | 34

2.0E+04 3.0E+04 4.0E+04 5.0E+04 6.0E+04 7.0E+04 8.0E+040

0.10.20.30.40.50.60.70.80.9

1

Reynolds Number, NRe

Hea

d L

oss,

hm (

m)

Figure 4.3: Head loss, hm(experimental)Vs Reynolds Number, NRe for1.0 inch 90° bend

1.2E+04 1.4E+04 1.6E+04 1.8E+04 2.0E+04 2.2E+04 2.4E+040123456789

Reynolds Number, NRe

Min

or L

oss C

o-ef

ficie

nt, K

Figure 4.4: Minor Loss Coefficient, K (experimental) Vs Reynolds Number, NRe for 0.5 inch 90° bend

Page | 35

2.5E+04 3.0E+04 3.5E+04 4.0E+04 4.5E+04 5.0E+04 5.5E+04 6.0E+04 6.5E+040

0.5

1

1.5

2

2.5

3

Reynolds Number, NRe

Min

or L

oss C

o-ef

ficie

nt, K

Figure 4.5: Minor Loss Coefficient, K (experimental) Vs Reynolds Number, NRe for 0.75 inch90° bend

2.0E+04 3.0E+04 4.0E+04 5.0E+04 6.0E+04 7.0E+04 8.0E+040

0.51

1.52

2.53

3.54

Reynolds Number, NRe

Min

or L

oss C

o-ef

ficie

nt, K

Figure 4.6:Minor Loss Coefficient, K (experimental) vs Reynolds Number, NRe for 1.0 inch 90°bend

Page | 36

4.4: SAMPLE CALCULATION

The calculation tables presented in the previous section have been constructed from the calculations is shown below. One sample calculation for the minor loss coefficient of a Galvanized Iron (GI) 90°bend is presented below:

Sample calculation is shown for 1.0 inch 90°bend for observation no. 1 of table.

Diameter, D = 1.0 inch

= 2.54 ×10-2 ×1.0 m

= 0.0254 m

Area of flow, A =п4 D2

= п4 × (0.0254)2

= 0.000506m2

Room Temperature, T = 25° C

Density of water, ρ = 996.95 kg/ m3

Dynamic viscosity, µ = 0.88× 10-3 Ns/m2

Density of manometric fluid (Carbon tetrachloride, CCl4), ρm= 1590 kg/ m3

Specific weight of manometric fluid (Carbon tetrachloride, CCl4), γm = 1590×9.81 N/m3

=15597.9 N/m3

Manometric deflection, Hm = 22 inch of CCl4

= 0.5588 m

Page | 37

Mass of water collected, m = 15.85 kg

Time of collection, t = 12.77 s

Mass flow rate, Q = mt

=15.8512.77

= 1.29 kg/s

Mean velocity of flow, v = QAρ

= 1.290.00050 6× 996.9 5

= 2.56m/s

Reynolds Number, NRe =ρvdµ

= 996.95 ×2.56 ×0.02540.88 ×10−3

= 73665.54

Head loss, hm(flowingfluid) =Hm(manometric fluid )× γ m(manometric fluid )γ (flowingfluid )

= 0.5588× 15597.9996.9 5× 9.81

= 0.89 m of water

Minor loss coefficient, K = 2gh m

v ²

Page | 38

= 2× 9.81× 0.89

(2.5 6) ²

= 2.66

CHAPTER 05

RESULTS AND DISCUSSION

Page | 39

5.1: RESULTS

The values of minor loss coefficients are tabulated for different Galvanized Iron (GI) 90° bends.

Table 5.1: Experimental value of minor loss coefficient for different GI 90° bends

90° bend dimension

Average value ofReynolds

Number,NRe

Average value of minor loss,hm (m)

Average value of minor loss

coefficient, K0.5 inch 17349.9 0.495 6.76949

0.75 inch 43529.8 0.56 2.06

1.0 inch 50355.7 0.566 3.061

Page | 40

5.2 DISCUSSION

GRAPH ANALYSIS

5.2.1: MINOR LOSS COEFFICIENT Vs REYNOLDS NUMBER

1.2E+04 1.4E+04 1.6E+04 1.8E+04 2.0E+04 2.2E+04 2.4E+040

1

2

3

4

5

6

7

8

9

Reynolds Number, NRe

Min

or L

oss C

o-effi

cien

t, K

Figure 5.1: Minor Loss Coefficient, K (experimental) Vs Reynolds Number, NRe for 0.50 inch 90° bend.

From the figure 5.1 it is observed that in case of 90° bend 1.0 inch to 0.75 inch diameter, the minor loss coefficient gradually decreases with the Reynolds number. Here, ten observations were taken and the range of Reynolds number was from about 13× 103 to 22× 103. Higher the Reynolds number, lower the minor loss coefficients.

The other two curves of 90° bends 0.75 inch and 1.0 inch also show the same characteristics although, in their case, the graphs show an increasing trend before minor loss coefficient starts to decrease with the Reynolds number. This phenomenon can be explained by Darcy-Weisbach equation:

hf = f× LD × v ²

2 g

Page | 41

1.0E+04 2.0E+04 3.0E+04 4.0E+04 5.0E+04 6.0E+04 7.0E+04 8.0E+040

1

2

3

4

5

6

7

8

9

0.5 inch

Reynolds Number, NRe

Min

or L

oss C

o-effi

cien

t, K

Figure 5.2: Minor loss coefficient (K) Vs Reynolds Number (NRe) for different dimensions.

From this equation it can be seen that major loss is proportional to the length of the system. But in case of a 90° bend or any type of joints or fittings such as elbows, valves etc. lengths of these devices are very small and hence major loss is negligible. So, at low velocity or low Reynolds number, major loss is negligible. But at higher velocity the major loss cannot be neglected, because it is proportional to the square of the velocity. So, major loss plays a greater role in frictional loss and minor loss tends to be less dominant. So, for higher Reynolds number, the head loss calculated directly from the manometric deflection contains a significant amount of major loss. As we have taken only the minor loss in our calculation, the minor loss coefficient has gradually decreased with higher Reynolds number. The expression used to calculate minor losses which is,

hm= K v ²2 g

As we can see from this equation, minor loss co-efficient K is inversely proportional to the square of velocity. So, as the velocity increases, so does Reynolds number but minor loss co-efficient decreases.

Page | 42

5.2.1: MINOR HEAD LOSS Vs REYNOLDS NUMBER

0.0E+00 1.0E+04 2.0E+04 3.0E+04 4.0E+04 5.0E+04 6.0E+04 7.0E+04 8.0E+040

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.5 inchPoly-nomial (0.5 inch)

Reynolds Number, NRe

Head

Los

s, hm

(m

)

Figure 5.3: Minor head loss (hm) Vs Reynolds Number (NRe) for different dimensions.

From the figure 5.3, the following observations can be made: The minor head loss increases with the increase in Reynolds number for all the 90°

bends. These phenomenon occur due to the fact that according to minor head loss formula, head loss is proportional to the square of velocity. It leads to the conclusion that higher the velocity as well as the Reynolds number, higher the amount of head losses.

As the diameter decreases, curve becomes steeper. Head loss generally increases with the decrease of diameter for a given Reynolds number. It can be explained as follows. When the inside diameter is made larger, the flow area increases and the velocity of the liquid at a given flow rate is reduced. When the velocity is reduced there is lower minor head loss. On the other hand, if the inside diameter of the pipe is reduced, the flow area decreases, the velocity of the liquid increases and the head loss due to friction increases.

Page | 43

CHAPTER 06

CONCLUSION AND SCOPE FOR FUTURE WORK

Page | 44

6.1 CONCLUSION

This section concludes the study of the minor losses in 90° bends of diameters 1.0 inch, .75 inch, .50 inch. The following conclusions can be made:

The thesis work focuses on the minor losses occurred in locally made bends. Therefore, it will be beneficial for the local people to use the data while using these bends.

Minor loss coefficient shows a decreasing trend for 0.5 inch diameter elbow with respect to Reynolds number but shows an increasing-decreasing pattern for 0.75 inch and 1 inch diameter elbows.

Minor Head loss generally shows an increasing trend with respect to Reynolds number for a given bend diameter.

Page | 45

6.2SCOPE FOR FUTURE WORKS

Some guideline for future work is as follows

1. The thesis work center on the minor losses occurred in locally available 90° bends. Therefore it will be beneficial to determine total head loss, both minor and frictional loss developed in a piping system using 90° bend and finally required power of the piping system.Further research can be carried out on 45° elbows, Tee joints and reducers to evaluate their loss characteristics.

2. The Platform-Scale used for this experiment is an outdated measuring technology. It was definitely prime source of error in measuring mass flow rate. It should be replaced by more modern measuring device like Nutating Disk Meter, Turbine flow Meter, Variable Area Meter (Rotameter) etc.

3. Manometric fluid other than Carbon tetrachloride can be used for much higher Reynolds number to determine higher head loss, as Hg manometer shows very small deflection due to large change in pressure. Again Water Manometer can be used to capture the head loss for small flow rate as water manometer shows very high deflection due to small change in pressure.

4. Further experiment must be conducted on more diameters (d) and materials. So that an empirical co-relation between Minor Loss Co-efficient (k) and Reynolds Number (NRe) can be developed. Present study concluded that K has an inverse relation with NRe.

5. Further experiment should he conducted to find out the velocity profile. Modern simulation software can be introduced to make a model of the total system that gives a univocal presentation of pressure and velocity profile.

Page | 46

REFERENCES

[1] V. L. Streeter, E. Benjamin Wylie, Fluid Mechanic. First ST Metric Edition, McGraw-HiII Book .Co; Singapore.

[2] P.N. Modi, S.M. Seth, Hydraulic and Fluid Mechanics Including Hydraulic Machines, Fourteenth edition 2002, Standard Book House.

[3] Quamrul Islam. A.K.M. Sadrul Islam. Fluid Mechanics Laboratory Practice, World University Service Press, ISBN 984-518-000-0

[4] M.H. Khan, Md. Quamrul Islam. "An Experimental Investigation of Flow Through Flexible Pipes and Bends", Journal of Institution of Engineers, Bangladesh, Vo17, No. 3 July, 1979.

[5] F.M. White, Fluid Mechanics, 5th ed., McGraw-Hill, New York, 2003.

[6] Z. H. Ayub, S. F. Al-Fahed, "The effect of gap width between horizontal tube and twisted tape on the pressure drop in turbulent water flow. Int. J. Heat and Fluid Flow", Vol. 14, No. 1, March 1993.

[7] Anthony Esposito, Fluid Power with Application, 6th Edition.

[8] Md. Hafizurrahman, A. K. Roy, Md. S. Hossain, "Determination of Minor head Loss and Friction Factor for locally Available PVC pipe 90°s". BUET, September-2009.

[9] Md. Rokonuzzarnan Khan, Saad Ahmed, A. S. M. Jonayak "Determination of friction Factor of Flow through Flexible Pipes and Minor Loss Coefficient of Flexible Bends", BUET, February-2011.

Page | 47

APPENDICES

APPENDIX A

Properties of liquids at standard atmosphere in SI unit

Page | 48

APPENDIX B

Page | 49